College Algebra – Challenge Problem 4
Name: _______________________________
Directions: Show all work and reasoning to receive full credit.
a) A ball is thrown from an initial height of 5 feet. After the ball travels 1 foot horizontally, its height is 6.75
feet. Then, after it travels another foot horizontally, the height is 8 feet.
i) Given the data above, use a graphing utility to find the quadratic equation that best represents the
path of the ball.
ii) Algebraically find the maximum height the ball will reach.
iii) Algebraically find how far the ball will travel horizontally before it hits the ground.
b) A volleyball is served from an initial height of one meter. After traveling horizontally 2 meters, the ball
reaches a height of 1.68m. Then after it travels horizontally another 2 meters, it reaches a height of 2.2m.
i) Given the data above, use a graphing utility to find the quadratic equation representing the path of
the serve.
ii) If a regulation volleyball court is 18 meters long and 9 meters wide, the top of the net is 2.43
meters from the ground, and the server was standing a meter behind the boundary line when serving,
prove that the serve made it over the net. SHOW ALL WORK AND JUSTIFY!
iii) The opposing team misses the serve and the ball hits the ground. Which teams gains a point, the
serving team or the opposing team? (Remember: if it’s in bounds the serving team gets a point, if it’s
out of bounds the opposing team gets a point.) You may use a calculator, but JUSTIFY YOUR
ANSWER!